Georgi–Glashow model

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Since the Georgi–Glashow model combines leptons and quarks into single irreducible representations, there exist interactions which do not conserve baryon number, although they still conserve B-L. This yields a mechanism for proton decay, and the rate of proton decay can be predicted from the dynamics of the model. However, proton decay has not yet been observed experimentally, and the resulting lower limit on the lifetime of the proton contradicts the predictions of this model. However, the elegance of the model has led particle physicists to use it as the foundation for more complex models which yield longer proton lifetimes.

These monopoles have quantized Y magnetic charges. Since the electromagnetic charge Q is a linear combination of some SU(2) generator with Y/2, these monopoles also have quantized magnetic charges, where by magnetic here, we mean electromagnetic magnetic charges.

To prevent unwanted couplings in the supersymmetric version of the model, we assign a Z2matter parity to the chiral superfields with the matter fields having odd parity and the Higgs having even parity. This is unnecessary in the nonsupersymmetric version, but then, we can't protect the electroweak Higgs from quadratic radiative mass corrections. See hierarchy problem. In the nonsupersymmetric version the action is invariant under a similar Z2 symmetry because the matter fields are all fermionic and thus must appear in the action in pairs, while the Higgs fields are bosonic.

A generic invariant renormalizablesuperpotential is a (complex) invariant cubic polynomial in the superfields. It is a linear combination of the following terms:

The first column is an Abbreviation of the second column (neglecting proper normalization factors), where capital indices are SU(5) indices, and i and j are the generation indices.

The last two rows presupposes the multiplicity of Nc is not zero (i.e. that a sterile neutrino exists). The coupling Hu 10i 10j has coefficients which are symmetric in i and j. The coupling NciNcj has coefficients which are symmetric in i and j. Note that the number of sterile neutrinogenerations need not be three, unless the SU(5) is embedded in a higher unification scheme such as SO(10).

The gauge algebra 24 decomposes as . This 24 is a real representation, so the last two terms need explanation. Both and are complex representations. However, the direct sum of both representation decomposes into two irreducible real representations and we only take half of the direct sum, i.e. one of the two real irreducible copies. The first three components are left unbroken. The adjoint Higgs also has a similar decomposition, except that it is complex. The Higgs mechanism causes one real HALF of the and of the adjoint Higgs to be absorbed. The other real half acquires a mass coming from the D-terms. And the other three components of the adjoint Higgs, , and acquire GUT scale masses coming from self pairings of the superpotential, aΦ2+b<Φ>Φ2.

The sterile neutrinos, if any exists, would also acquire a GUT scale Majorana mass coming from the superpotential coupling νc2.

Because of matter parity, the matter representations and 10 remain chiral.

It's the Higgs fields 5H and which are interesting.

The two relevant superpotential terms here are and . Unless there happens to be some fine tuning, we would expect both the triplet terms and the doublet terms to pair up, leaving us with no light electroweak doublets. This is in complete disagreement with phenomenology. See doublet-triplet splitting problem for more details.

After some twenty-five years, we are still waiting. No protons have decayed. We have been waiting long enough to know that SU(5) grand unification is wrong. It's a beautiful idea, but one that nature seems not to have adopted. Page 64.

Indeed, it would be hard to underestimate the implications of this negative result. SU(5) is the most elegant way imaginable of unifying quarks with leptons, and it leads to a codification of the properties of the standard model in simple terms. Even after twenty-five years, I still find it stunning that SU(5) doesn't work. Page 65.

When the filmmaker Sandy Bates (played by Woody Allen) in the 1980 Woody Allen film Stardust Memories launches a depressive soliloquy with the quote, "Did anybody read on the front page of The Times that matter is decaying?", this was almost certainly a reference to the Georgi–Glashow model, given the film's period, the importance of the Georgi–Glashow model at the time and the many contemporary layperson articles in circulation about some of the model's most striking consequences, particularly its mechanism for proton decay. An actual New York Times article[1] appeared two years later, fulfilling Allen's blackly humorous foreshadowing of a world whose news was so baleful that the mainstream media were systematically reporting its material demise.